CN112762925A - Low-orbit satellite attitude determination method based on geomagnetism meter and gyroscope - Google Patents

Abstract

The invention belongs to the field of low-orbit satellite attitude determination, and particularly relates to a low-orbit satellite attitude determination method based on a magnetometer and a gyroscope, which comprises the following steps: acquiring initial low-orbit satellite attitude parameters before the low-orbit satellite is launched, and measuring a geomagnetic field by using a geomagnetic meter carried on the low-orbit satellite; calculating the attitude of the low-orbit satellite by adopting an attitude algorithm; establishing a four-element attitude updating equation of a gyroscope, and updating the attitude of the low-earth orbit satellite in real time; fusing the low-orbit satellite attitude and the low-orbit satellite attitude updated by the gyroscope by adopting an extended Kalman filtering equation, and outputting a low-orbit satellite attitude angle with higher precision; the method provides a high-precision data source for the low-orbit satellite orbit control without depending on systems such as an external GNSS and the like, and avoids the uncontrollable performance of the low-orbit satellite in orbit transfer when the low-orbit satellite is disconnected with the ground.

Description

A low-orbit satellite attitude determination method based on geomagnetometer and gyroscope

technical field

The invention belongs to the field of low-orbit satellite attitude determination, in particular to a low-orbit satellite attitude determination method based on a geomagnetometer and a gyroscope.

Background technique

At present, there are mainly four kinds of high-precision low-orbit satellite orbit and attitude determination techniques, including satellite laser ranging (Satellite Laser Ranging, SLR), Doppler Orbitography and Radiolocation Integrated Satellite (DORIS), precision measurement Distance and speed measurement technology (PreciseRange and Range-Rate Equipment, PRARE) and global positioning technology (GlobalNavigationSatellite System, GNSS). However, SLR is expensive, heavy equipment, and due to the limited observation coverage area and severe weather effects, it is difficult to perform the precise orbit determination of low-orbit satellites at an altitude of about 500km alone. The data acquisition and processing speed of the DORIS system in France is relatively slow, and the coverage of the ground tracking network is relatively weak. Germany's PRARE system has fewer stations in the world, and the equipment is more expensive, and the number of satellites loaded with the system is small. However, GNSS cannot cope with the requirements of orbit determination and attitude determination in extraordinary periods such as failure, and cannot achieve orbit determination and attitude determination in the whole arc during the working period. There are still many difficulties in the method and system of autonomous orbit determination and attitude determination of low-orbit satellites based on non-navigation satellite signals.

When determining the attitude of the low-orbit satellite, the precise measurement of the roll angle, pitch angle and heading angle of the low-orbit satellite, and the attitude of the low-orbit satellite machine with reference to the roll angle, pitch angle and heading angle can be more accurate. Good control of the motion state and trajectory of low-orbit satellites. However, due to the limitation of volume, mass, power consumption and other factors, the traditional low-orbit satellite attitude measurement method cannot meet the requirements of low-orbit satellite attitude measurement. Therefore, a method that can measure the attitude of low-orbit satellites more accurately is urgently needed.

SUMMARY OF THE INVENTION

In order to solve the above problems existing in the prior art, the present invention proposes a low-orbit satellite attitude determination method based on a geomagnetometer and a gyroscope, and the method includes:

S1: Obtain the initial attitude parameters of the low-orbit satellite;

S2: establish the orbital coordinate system of the low-orbit satellite, use the gyroscope to measure the satellite angular velocity of the low-orbit satellite in this coordinate system, and use the geomagnetometer to measure the geomagnetic component of the low-orbit satellite in this coordinate system;

S3: Input the satellite angular velocity into the four-element attitude update model of the gyro, calculate the attitude information of the low-orbit satellite, and obtain the state of the satellite at the next moment;

S4: Input the geomagnetic component and the attitude information of the low-orbit satellite in the coordinate system of the low-orbit satellite into the attitude measurement model of the geomagnetometer, and obtain the observation equation of the low-orbit satellite;

S5: The extended Kalman filter fusion algorithm is used to process the measured observation equation to obtain the multi-point information of the low-orbit satellite;

S6: Continuously correct the attitude information of the low-orbit satellite by iterating and filtering the multi-point information of the low-orbit satellite;

S7: Determine whether the low-orbit satellite attitude determination task is over, that is, whether the satellite has reached a predetermined attitude, and if the conditions are not met, return to S2.

卫星俯仰角θ、卫星航向角ψ；Preferably, the initial low-orbit satellite attitude parameters before the launch of the low-orbit satellite include: satellite roll angle

Satellite pitch angle θ, satellite heading angle ψ;

Preferably, the four-element attitude update model of the gyro is:

Preferably, the four-element state equation of attitude is:

X(k+1)=F·X(k)+V

Further, the expression of the state transition equation F is:

Preferably, the small-angle geomagnetometer attitude measurement model is:

Preferably, the observation equation of the low-orbit satellite is:

Y(k+1)=HX(k+1)+N

Preferably, using the extended Kalman filter fusion algorithm to process the measured attitude includes: using the covariance update formula to update the observation equation, calculating the gain matrix of the updated observation equation, and performing the attitude information of the low-orbit satellite according to the gain matrix. renew;

The covariance update equation is:

P ^- (k+1)=FP(k)F ^T +R

P(k+1)=[IK(k+1)H(k+1)]P ^- (k+1)

The gain matrix is:

K(k+1)=P ^- (k+1)H[HP ^- (k+1)H ^T +Q] ^-1

The state update equation is:

X(k+1)=X ^- (k+1)+K(k+1)(Y(k+1)-HX ^- (k+1))

Preferably, the process of iterating and filtering the multi-point information of the low-orbit satellite includes: calculating the initial four elements in combination with the initial attitude of the low-orbit satellite, using the gyroscope to update the four elements, and using the extended Kalman filter fusion algorithm to tune the gyroscope. The accumulated error of the instrument is corrected, and the attitude angle of higher precision is output.

The present invention can complete high-precision low-orbit satellite attitude measurement on the premise of consuming less low-orbit satellite resources; the present invention provides high-precision low-orbit satellite orbit control without relying on external GNSS and other systems. It avoids the uncontrollability of low-orbit satellites changing orbits when the low-orbit satellites lose contact with the ground.

Description of drawings

Fig. 1 is a flowchart of the present invention;

Fig. 2 is the result diagram of the heading angle fusion of the attitude angle of the specific implementation case of the present invention;

Fig. 3 is the roll angle fusion result diagram of the attitude angle of the specific implementation case of the present invention;

FIG. 4 is a result diagram of the pitch angle fusion result of the attitude angle in a specific implementation case of the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

A low-orbit satellite attitude determination method based on a geomagnetometer and a gyroscope, as shown in Figure 1, the method includes:

S1: Obtain the initial low-orbit satellite attitude parameters before the launch of the low-orbit satellite;

S2: Use a gyroscope to measure the satellite angular velocity in the low-orbit satellite's own coordinate system, and use a geomagnetometer to measure the geomagnetic component in the low-orbit satellite's own coordinate system;

S3: The attitude information of the low-orbit satellite is obtained by using the four-element attitude update model of the gyro and the attitude measurement model of the geomagnetic meter;

S4: According to the satellite angular velocity, the attitude information of the low-orbit satellite is calculated using the attitude four-element state equation, and the state of the satellite at the next moment is obtained; the attitude measurement equation of the geomagnetometer is established according to the geomagnetic component in the coordinate system of the low-orbit satellite body, and the next Attitude measurement based on the state of the satellite at the moment;

S5: The extended Kalman filter fusion algorithm is used to process the measured attitude to obtain the multi-point information of the low-orbit satellite;

S6: Continuously correct the attitude information of the low-orbit satellite by iterating and filtering the multi-point information of the low-orbit satellite;

S7: Determine whether the low-orbit satellite attitude determination task is over, if not, return to S2.

卫星俯仰角θ、卫星航向角ψ。The initial low-orbit satellite attitude parameters before the launch of the low-orbit satellite include: satellite roll angle

Satellite pitch angle θ, satellite heading angle ψ.

As shown in Figure 2, it is the result of heading angle fusion of the attitude angle of the present invention. In this figure, the * model line represents the heading angle information obtained by using the magnetometer model alone, and the model line represents the heading obtained by using the gyroscope model alone to update. Angle information, the solid line represents the heading angle information obtained by the fusion of the two.

As shown in Figure 3, it is the result diagram of the roll angle fusion result of the attitude angle of the present invention. In the figure, the * shape line represents the roll angle information obtained by using the magnetometer model alone, and the shape line represents the update obtained by using the gyroscope model alone. The roll angle information of , the solid line represents the roll angle information obtained by the fusion of the two.

As shown in Figure 4, it is the result diagram of the pitch angle fusion of the attitude angle of the present invention, in this figure, the * type line represents the pitch angle information obtained by using the magnetometer model alone, and the type line represents the pitch angle obtained by using the gyroscope model alone to update. Angle information, the solid line represents the pitch angle information obtained by the fusion of the two.

In the gyroscope three-axis gyroscope of the present invention, the geomagnetometer is a three-axis geomagnetometer; the three-axis gyroscope and the three-axis geomagnetometer are installed along the coordinate system of the low-orbit satellite body. In the present invention, the sensitive data of the gyroscope and the geomagnetic meter are synchronized in time.

The process of constructing the four-element attitude update model of the gyro is as follows:

表示滚角，θ表示俯仰角，ψ表示航向角，q₀、q₁、q₂、q₃分别为四元素。in,

represents the roll angle, θ represents the pitch angle, ψ represents the heading angle, and q ₀ , q ₁ , q ₂ , and q ₃ are four elements respectively.

The process of constructing the geomagnetometer attitude measurement model is as follows:

Among them, B _x , _{By , and B z represent} the measured values of the magnetic intensity in the measurement coordinates, respectively, and B _bx , B _by , and B _bz represent the geomagnetic components in the low-orbit satellite body coordinate system, respectively.

The four-element state equation of attitude is:

X(k+1)=F·X(k)+V

Among them, X(k)=[q ₀ (k) q ₁ (k) q ₂ (k) q ₃ (k)] ^T represents the four elements of attitude, F represents the state transition equation, and V represents the Gaussian white noise with zero mean .

The formula for calculating the state transition equation F is:

Among them, ω _x , ω _y , and ω _z are the measured values of the three-axis angular velocity of the low-orbit satellite in the body coordinates of the low-orbit satellite, respectively, and Δt is the time variation.

According to the Gaussian white noise V with zero mean, the covariance of the four-element state equation of attitude is calculated, and the expression of the covariance is shown as:

E{VV ^T }=R

Among them, E{.} represents the calculation of covariance, R represents the covariance of the four-element state equation of attitude, and V ^T represents the Gaussian white noise transposed matrix.

According to the IGRF geomagnetic field model, the observation equation of the relationship between the geomagnetic field vector and the attitude of the low-orbit satellite is established:

Y(k+1)=HX(k+1)+N

Y(k+1) represents the magnetic intensity matrix under the measurement coordinates, H represents the observation matrix, and N represents the Gaussian white noise with zero mean. in:

Calculate the covariance of the observation equation of the attitude relationship of the low-orbit satellite according to the Gaussian white noise N with a mean value of zero; its expression is:

E{NN ^T }=Q

Among them, E{.} represents the calculation of covariance, Q represents the covariance of the observation equation of the low-orbit satellite, and N ^T represents the Gaussian white noise transposed matrix.

为地磁场矢量在轨道坐标系和测量坐标下的转换关系，转换关系为：

is the conversion relationship of the geomagnetic field vector in the orbital coordinate system and the measurement coordinate, the conversion relationship is:

Among them, B _x , _{By , and B z represent} the three-axis components of geomagnetic intensity in orbital coordinates, and B _bx B _by B _bz represent the measured value of geomagnetic intensity when the geomagnetometer is installed along the low-orbit satellite body coordinate system.

俯仰角θ、航向角ψ，其表达式为：Calculate the roll angle in the attitude angle of the low-orbit satellite according to the conversion relationship of the geomagnetic field vector in the orbital coordinate system and the measurement coordinate

The pitch angle θ and the heading angle ψ are expressed as:

θ=arcsin[2(q ₀ q ₂ -q ₁ q ₃ )]

The process of iterating and filtering the multi-point information of the low-orbit satellite includes: combining the initial attitude of the low-orbit satellite, solving the initial four elements, using the gyroscope to update the four elements, and using the extended Kalman filter fusion combined with the magnetometer information The algorithm corrects the accumulated error of the gyroscope, thereby outputting the attitude angle with higher precision.

The covariance calculation equation in the fusion process is expressed as:

P ^- (k+1)=FP(k)F ^T +R

The corresponding gain matrix expression is:

K(k+1)=P ^- (k+1)H[HP-(k+1)H ^T +Q] ^-1

The covariance is updated according to the covariance expression and the gain matrix, and the expression is:

P(k+1)=[IK(k+1)H(k+1)]P ^- (k+1)

The attitude of the low-orbit satellite is updated according to the gain matrix and the covariance expression, and the update expression is:

X(k+1)=X ^- (k+1)+K(k+1)(Y(k+1)-HX ^- (k+1))

Among them, P ^- (k+1) represents the antecedent error covariance at time k+1, k represents the sampling time, F represents the state transition equation, R represents the value of the covariance of the four-element state equation of attitude, T represents the transposition, and K (k+1) represents the gain matrix at time k+1, H(k+1) represents the observation matrix, Q represents the covariance of the observation equation of the low-orbit satellite, and X ^- (k+1) represents the front attitude at time k+1 Four-element equation of state.

The invention provides a low-orbit satellite attitude determination technology combined with a geomagnetometer/gyroscope. Using this technology to measure the attitude of low-orbit satellites can provide accurate data sources for low-orbit satellite motion control, and at the same time achieve precise control of low-orbit satellite orbits, so as to ensure that the ground measurement and control station can stably track low-orbit satellites. The related applications of low-orbit satellites are guaranteed.

The above-mentioned embodiments further describe the purpose, technical solutions and advantages of the present invention in detail. It should be understood that the above-mentioned embodiments are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modification, equivalent replacement, improvement, etc. made to the present invention within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims (9)

1. a low-orbit satellite attitude determination method based on geomagnetometer and gyroscope, is characterized in that, this method comprises: S1: Obtain the initial attitude parameters of the low-orbit satellite; S2: establish the orbital coordinate system of the low-orbit satellite, use the gyroscope to measure the satellite angular velocity of the low-orbit satellite in this coordinate system, and use the geomagnetometer to measure the geomagnetic component of the low-orbit satellite in this coordinate system; S3: Input the satellite angular velocity into the four-element attitude update model of the gyro, calculate the attitude information of the low-orbit satellite, and obtain the state of the satellite at the next moment; S4: Input the geomagnetic component and the attitude information of the low-orbit satellite in the coordinate system of the low-orbit satellite into the attitude measurement model of the geomagnetometer, and obtain the observation equation of the low-orbit satellite; S5: The extended Kalman filter fusion algorithm is used to process the measured observation equation to obtain the multi-point information of the low-orbit satellite; S6: Continuously correct the attitude information of the low-orbit satellite by iterating and filtering the multi-point information of the low-orbit satellite; S7: Determine whether the low-orbit satellite attitude determination task is over, that is, whether the satellite has reached a predetermined attitude, and if the conditions are not met, return to S2. 2. a kind of low-orbit satellite attitude determination method based on geomagnetometer and gyroscope according to claim 1, is characterized in that, the initial low-orbit satellite attitude parameter before low-orbit satellite launch comprises: satellite roll angle

The satellite pitch angle θ and the satellite heading angle ψ are determined by the ground auxiliary equipment at the initial start-up. 3. a kind of low-orbit satellite attitude determination method based on geomagnetometer and gyroscope according to claim 1, is characterized in that, the four-element attitude update model of gyro is:

θ=arcsin[2(q ₀ q ₂ -q ₁ q ₃ )],

Calculate the attitude angle through the four elements, and use the gyroscope angular velocity to update the four elements; in,

represents the roll angle, _θ represents the _{pitch angle} , and _{ψ represents} the _{heading angle} . Shaft angular velocity measurement. 4. a kind of low-orbit satellite attitude determination method based on geomagnetometer and gyroscope according to claim 1, is characterized in that, the four-element state equation of attitude is: X(k+1)=F·X(k)+V X(k)=[q ₀ (k) q ₁ (k) q ₂ (k) q ₃ (k)] ^T Among them, X(k) represents the four-element attitude, F represents the state transition equation, V represents the Gaussian white noise with zero mean, and the covariance is E{VV ^T }=R, T represents the transposition, and R represents the four-element state equation of attitude covariance of . 5. a kind of low-orbit satellite attitude determination method based on geomagnetometer and gyroscope according to claim 4, is characterized in that, the expression of state transition equation F is:

Among them, ω _x , ω _y , and ω _z are the measured values of the three-axis angular velocity of the low-orbit satellite in the body coordinates of the low-orbit satellite, respectively, and Δt is the time variation. 6. a kind of low-orbit satellite attitude determination method based on geomagnetometer and gyroscope according to claim 1, is characterized in that, geomagnetometer attitude measurement model is:

Among them, B _x , _{By , and B z represent} the measured values of the magnetic intensity in the measurement coordinates, respectively, and B _bx , B _by , and B _bz represent the geomagnetic components in the low-orbit satellite body coordinate system, respectively. 7. a kind of low-orbit satellite attitude determination method based on geomagnetometer and gyroscope according to claim 1, is characterized in that, the observation equation of low-orbit satellite is: Y(k+1)=HX(k+1)+N

Among them, Y(k+1) represents the magnetic intensity matrix under the measurement coordinates, H represents the observation matrix, N represents the Gaussian white noise with zero mean, and its covariance is E{NN ^T }=Q, T represents the transposition, and Q represents the The covariance of the observation _equation of the low-orbit satellite, B _x , By , and B _z represent the magnetic intensity measurement values under the measurement coordinates, respectively. 8. a kind of low-orbit satellite attitude determination method based on geomagnetometer and gyroscope according to claim 1, is characterized in that, described adopting extended Kalman filter fusion algorithm to measure the attitude that obtains to process comprises: Use the covariance update formula to update the observation equation, calculate the gain matrix of the updated observation equation, and update the attitude information of the low-orbit satellite according to the gain matrix; The covariance update equation is: P ^- (k+1)=FP(k)F ^T +R P(k+1)=[IK(k+1)H(k+1)]P ^- (k+1) The gain matrix is: K(k+1)=P ^- (k+1)H(k+1)[H(k+1)P ^- (k+1)H ^T (k+1)+Q] ^-1 The state update equation is: X(k+1)=X ^- (k+1)+K(k+1)(Y(k+1)-HX ^- (k+1)) Among them, P ^- (k+1) represents the antecedent error covariance at time k+1, k represents the sampling time, F represents the state transition equation, R represents the value of the covariance of the four-element state equation of attitude, T represents the transposition, and K (k+1) represents the gain matrix at time k+1, H(k+1) represents the observation matrix, Q represents the covariance of the observation equation of the low-orbit satellite, and X ^- (k+1) represents the front attitude at time k+1 Four-element equation of state. 9. a kind of low-orbit satellite attitude determination method based on geomagnetometer and gyroscope according to claim 1, is characterized in that, the process that the multi-point information of low-orbit satellite is carried out iterative and filtering processing comprises: according to low-orbit satellite initial In the initial four elements of attitude calculation, the gyroscope is used to update the four elements, and the extended Kalman filter fusion algorithm is used to correct the accumulated error of the gyroscope, and output a higher-precision attitude angle.

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